Is it a correct math definition of averaging two vectors? (Blender vector math node)
The Average operator was initially added to Blender as a way to get a Unit Angle Bisector, which is a unit vector that bisects the angle between the two input vectors. The operator assumes that both input vectors are unit vectors, otherwise, it will not work as expected.

Due to the misleading name and the ambiguity of operation. The Average operator has been removed in Blender 2.81. Thought it might be added again in the future in a more clear form.